The following definitions are quoted from [1]}. A class of triangles \(\xi \)  is closed under base change if for any triangle \(@C=1.5em{A[r]^f&B[r]^g&C[r]^{h\ \ \ \ }&\Sigma A}\)  in \(\xi \)  and any morphism \(@C=1.5em{\varepsilon : E[r]& C,}\) 
one gets from the commutative diagram of triangles
\({0 [d] [r] & M [d]_{\alpha } [r]^{=} & M[d]_{\delta } [r] & 0[d] \\A [d]_{||} [r]^{f^{\prime }} & G [d]_{\beta } [r]^{g^{\prime }} & E[d]_{\varepsilon } [r]^{h^{\prime }} & \Sigma A[d]_{||} \\A [d] [r]^{f} & B[d]_{\gamma } [r]^{g} & C [d]_{\zeta } [r]^{h} & \Sigma A [d] \\0 [r]& \Sigma M[r]^{=} & \Sigma M [r] & 0 }\) 
